An “option” is understood to be a contract that gives a buyer a right, but not an obligation, to buy or sell an underlying asset at a specific price on or before a certain date. An option pricing formula, known as the Black-Scholes option pricing formula, provides a theoretically consistent framework for pricing options. Option pricing theory is also known as Black-Scholes theory or derivatives pricing theory.
There are basically two types of options: calls and puts. A call gives a holder a right to buy an asset at a certain price within a specific period of time. A put gives a holder a right to sell an asset at a certain price within a specific period of time. Entities that buy options are called holders and those who sell options are called writers. Based on the two types of options and the two types of entities that trade in options, there are a total of four types of participants in the options markets: buyers of calls, sellers of calls, buyers of puts, and sellers of puts.
The price at which an underlying asset can be purchased or sold, according to the terms of the option, is called the “strike price.” This is the price an asset must go above (for calls) or go below (for puts) before a position can be exercised. The strike price is distinguished from the “spot price,” which is a current price at which a particular asset can be bought or sold at a specified time and place.
There are two classes of options: American and European. The classes are based on when an exercise can occur. An American option can be exercised at any time between its date of purchase and its expiration date. A European option can only be exercised at the end of its life. An option is worthless after its expiry or exercise date has passed. This holds true for both American and European options.
The calls and puts described above may be referred to as “plain vanilla” options. Plain vanilla options can be identified as standard options. There are, however, many different types and variations of options. Non-standard options are often called “exotic options.” Exotic options may use variations on payoff profiles of plain vanilla options or may differ in other respects from plain vanilla options. Exotic options may also include completely different products that nonetheless carry some type of option ability.
A “basket option” is one type of exotic option. In contrast to a plain vanilla option, the underlying asset of a basket option may consist of a number of assets. That is, NA≧1, where NA is the number of underlying assets of a basket option. Accordingly, a basket spot price is the sum of the spot prices of each individual asset. The underlying assets may be, for example, commodities, securities, or currencies. This list of possible underlying assets is not meant to be exclusive, but rather exemplary.
A calculation of a fair market value of an exotic option, such as a typical basket option, is a computationally complex task that presently, using known tools and methods such as Monte Carlo analysis, can take several hours using a personal computer. In financial analysis systems, such time intensive calculations typically have been performed periodically, for example, in a “back office area” of a banking organization.
In order to evaluate a Basket Option (“BO”) or an Average Spot Option (“ASpO”) there are two main approaches: analytical approximate approaches (using “closed form” nearby solutions) and Monte Carlo based ones (performing numerical simulations). An Average Spot Basket Option (“ASpBO”) can be evaluated by Monte Carlo (e.g., using the finance tool FinCad®) or by sequentially applying an analytical approximation for BO and an analytical approximation for ASpO. However, sequential application of a BO and an ASpO method in order to evaluate ASpBO neglects the correlation between spot prices of distinct underlying assets at distinct instants resulting in restricted accuracy. What is needed is a method to quickly and accurately evaluate a fair value, or approximation of a fair value, of exotic options, such as basket options that includes the effect of the correlation between spot prices of distinct underlying assets at distinct instants. It is also desirable to have a system, incorporating the desired method, which can be implemented on personal computers, which can provide accurate results in near real-time, or within a fraction of the time now taken by standard methods, such as Monte Carlo analyses.